Generators and Representations for G = U₃(8)

Standard generators

• Standard generators of U₃(8) are a and b where a has order 2, b has order 3 (necessarily in class 3C) and ab has order 19. (Source: ATLAS)
• Standard generators of 3.U₃(8) = SU₃(8) are preimages A and B where A has order 2 and AB has order 19. (Source: ATLAS)

BBOX programs

• Checker for U₃(8)
• CCL rep tester for U₃(8)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
U3(8)	56	-	No representations available
U3(8)	57	o	57(a)	χ3	Q(ω)			81%		23.3	perm rep on 1539 pts
			57(b)	χ4	Q(ω)			81%		23.3	complex conjugate of χ3
			114	χ3+χ4	Z			74%	72	58.5	perm rep on 1539 pts, LLL'ed
U3(8)	133	+	133(a)	χ5	Z			68%	225	84.1	perm rep on 3648 pts
			133(b)	χ6	Z			64%	129	84.3	perm rep on 3648 pts
			133(c)	χ7	Z			66%	258	84.8	perm rep on 3648 pts
3.U3(8)	57	o	No representations available
3.U3(8)	189	o	No representations available

Notes

We assume xy²xyxy²xyxy is in class 6B. We also assume the elements

• xy²xy²xyxy²xyxy²(xy)⁶
• xy²xyxy²xyxy²xy²(xy)⁶
• xy²xyxy²(xy)⁶

Last generated on Sat Sep 24 18:53:07 2005